Trouble with space-like noncommutative field theory

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Elsevier Science Bv
Google Scholar
Research Projects
Organizational Units
Journal Issue
It is argued that the one-loop effective action for space like noncommutative (i) lambda phi(4) scalar field theory and (ii) U(1) gauge theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and reinvestigating other types of noncommutativity.
© 2005 Elsevier B.V. All rights reserved. V.G. wishes to acknowledge the hospitality of the Department of Theoretical Physics of Universidad Complutense de Madrid. J.M.G.B. thanks MEC, Spain, for support through a ‘Ramón y Cajal’ contract. He also acknowledges discussions with E. López. F.R.R. is grateful to MEC, Spain, for financial support through grant BFM2002-00950.
Unesco subjects
[1] J. Gomis, T. Mehen, Nucl. Phys. B 591 (2000) 265. [2] M.A. Rieffel, Memoirs Am. Math. Soc. 506 (1993). [3] R. Estrada, J.M. Gracia-Bondía, J.C. Várilly, J. Math. Phys. 30 (1989) 2789. [4] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Clarendon Press, Oxford, 1997. [5] A.O. Barvinsky, G.A. Vilkovisky, Nucl. Phys. B 333 (1990) 471. [6] J.M. Gracia-Bondía, J.C. Várilly, H. Figueroa, Elements of Noncommutative Geometry, Birkhäuser, Boston, 2001. [7] L. Schwartz, Theórie des Distributions, Hermann, Paris, 1966. [8] F. Ruiz Ruiz, Nucl. Phys. B 637 (2002) 143. [9] C. Itzykson, J.-B. Zuber, Quantum Field Theory, McGraw Hill, New York, 1980, Section 6.2. [10] V. Gayral, hep-th/0412233. [11] F. Ruiz Ruiz, Phys. Lett. B 502 (2001) 274. [12] D. Bahns, S. Doplicher, K. Fredenhagen, G. Piacitelli, Phys. Rev. D 71 (2005) 025022, hep-th/0408204. [13] D. Bahns, S. Doplicher, K. Fredenhagen, G. Piacitelli, Phys. Lett. B 533 (2002) 178. [14] K. Fujikawa, hep-th/0410146. [15] A. Matusis, L. Susskind, N. Toumbas, JHEP 0012 (2000 002l; L. Alvarez-Gaumé, M.A. Vázquez-Mozo, Nucl. Phys. B 668 (2003) 293. [16] F. Ardalan, N. Sadooghi, Int. J. Mod. Phys. A 17 (2002) 123; A. Armoni, E. López, S. Theissen, JHEP 0206 (2002) 050.